切线圆弧光滑支持向量回归机收敛性研究

Research of Convergence for Tangent Circular Arc Smooth Support Vector Regression

传统支持向量机模型的目标函数是一个严格凸的二次规划函数,但是由于加号函数的不可微性,不能用通常的求解最优化问题算法.针对支持向量回归机模型,文中提出使用切线圆弧光滑函数替换原来目标函数中的加号函数,光滑化传统支持向量回归机模型的目标函数.分析了切线圆弧光滑函数的性质,证明了切线圆弧光滑支持向量回归机的收敛性,并且给出了满足精度要求时,光滑因子的取值方法.

Objective function of traditional Support Vector Machine is a strictly convex quadratic problem ,but is not differentiable due to plus function x＋ ,which precludes the most used optimization algorithms .For support vector regression model , this paper presents tangent circular arc smooth function to approximate plus function x＋ in original un-differentiable model ,and makes the objective function of traditional support vector regression machine smooth .Properties of tangent circular arc smooth function are analyzed ,convergence of tangent circular arc smooth support vector regression model is proved ,and how to determine the smallest value of smoothness factor α when meets the requirement of the preset precision is given .